This is so sad and I feel for your daughter and your ex - you obviously have a good relationship with him as does your daughter
Can your ex communicate at all? Have you tried to explain to him what will happen if he moves 200 miles away?
I really do not know what rights your 7 yr old has but you may benefit from a visit to the CAB. Some solicitors give the first half hour of their time free so maybe you could find one who can asnwer your question?
I hope you find some resolution to this for your daughters sake as well as your ex's
Best of luck